WASHINGTON—Days after the Trump administration instituted a controversial travel ban in January 2017, Google employees discussed ways they might be able to tweak the company’s search-related functions to show users how to contribute to pro-immigration organizations and contact lawmakers and government agencies, according to internal company emails.

The email traffic, reviewed by The Wall Street Journal, shows that employees proposed ways to “leverage” search functions and take steps to counter what they considered to be “islamophobic,...